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Weight-for-Length Percentile Calculator (WHO, 0-24 Months)

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WHO Weight-for-Length Growth Chart (0-24 Months, 45-110 cm)

Plot a child's weight against WHO reference data using recumbent length — not age — as the independent variable. The chart displays the standard percentile curves (3rd, 15th, 50th, 85th, 97th) for boys or girls and pins your child's point so you can see whether their weight is proportionate to their body size.

LMS Method: Z = ((X/M)^L - 1) / (L × S), percentile = Φ(Z) × 100

How It Works

The WHO 0-24 month weight-for-length chart answers a different question from weight-for-age: instead of asking "how does this child's weight compare to peers of the same age," it asks "how does this child's weight compare to peers of the same body length?" The calculator looks up three parameters from the WHO weight-for-length LMS table — L (skewness), M (the median weight at that length), and S (coefficient of variation) — for the child's exact recumbent length in centimeters, regardless of age. It then computes a Z-score using the Box-Cox equation Z = ((X/M)^L − 1) / (L × S) and maps that Z-score through the standard normal CDF to a percentile. The WHO table is indexed at one-millimeter (0.1 cm) resolution from 45 cm to 110 cm, which is how the WHO Anthro R package implements the lookup. Weight-for-length is the WHO primary screen for wasting (acute undernutrition) in children under 2.

Example Problem

A boy with a recumbent length of 70 cm weighs 8.5 kg. Where does he fall on the WHO weight-for-length chart for 0-24 months?

  1. Select Boy for sex and confirm the weight and length units (kg and cm in this example).
  2. Enter the recumbent length: 70.0 cm. Note that age is not used — only the measured length matters.
  3. Enter the weight: 8.5 kg.
  4. Look up the WHO weight-for-length LMS triple for boys at 70 cm: L ≈ -0.3521, M ≈ 8.4227 kg, S ≈ 0.08171.
  5. Compute the Z-score with Z = ((X/M)^L − 1) / (L × S). Substituting gives Z ≈ ((8.5/8.4227)^-0.3521 − 1) / (-0.3521 × 0.08171) ≈ 0.11.
  6. Map the Z-score through the standard normal CDF: Φ(0.11) ≈ 0.54, so the percentile is approximately the 50th.
  7. Report the result: a boy 70 cm long weighing 8.5 kg is at the WHO median weight for his length.

Key Concepts

Weight-for-length is a proportionality check, not an age check. A tall 12-month-old who is heavy for her age may be perfectly proportioned for her length; a short 12-month-old who looks average on weight-for-age may in fact be heavy-for-length. The WHO treats weight-for-length below the 3rd percentile (Z ≈ −2) as wasting and above the 97th (Z ≈ +2) as overweight that warrants follow-up. The measurement used here is recumbent length — measured lying flat on a board — not standing height. Standing height runs about 0.7 cm shorter than recumbent length in the same child, so mixing the two can shift percentiles. The WHO 0-24 month chart covers lengths from 45 cm to 110 cm (about 17.7 to 43.3 in); around age 2 (or once the child is measured standing), pediatricians switch to the WHO 2-5 year weight-for-height chart.

Applications

  • Well-child visits: pediatricians check weight-for-length at every visit 0-24 months to confirm proportional growth alongside weight-for-age and length-for-age.
  • Wasting screening: the WHO defines acute malnutrition as a weight-for-length Z-score below −2 (roughly the 3rd percentile); it is the primary WHO IMCI screen for infants under 2.
  • Overweight surveillance in infants: when weight-for-length exceeds the 97th percentile, the AAP recommends a nutritional conversation before the child reaches the toddler years.
  • Post-illness recovery: tracks whether an infant has regained proportional weight — not just raw grams — after a hospitalization or infectious illness.
  • Adoption and refugee intake: when date of birth is unknown or unreliable, weight-for-length gives a pediatrician a usable growth read without needing age.
  • NICU graduate follow-up: clinicians confirm that catch-up weight gain keeps pace with catch-up length instead of outstripping it.

Common Mistakes

  • Confusing weight-for-length with weight-for-age — they answer different questions; a child can be average on one and outside the normal range on the other.
  • Using standing height instead of recumbent length — standing measurements understate the child's length by about 0.7 cm and shift the percentile downward.
  • Entering length in inches without switching the unit selector — verify the unit dropdown matches the measurement before typing.
  • Using this chart for a child whose length exceeds 110 cm (about 43.3 in) — switch to the WHO 2-5 year weight-for-height chart once the child is being measured standing.
  • Treating a single high weight-for-length percentile as a diagnosis — a solidly built child may always sit above the 85th without being unhealthy; trajectory matters more than a single point.
  • Mixing charts mid-tracking — once you start a child on WHO weight-for-length, stay on it (and on recumbent length) until the transition at ~24 months to avoid artificial percentile jumps.

Frequently Asked Questions

What is the 50th percentile weight for a boy who is 70 cm long?

On the WHO 0-24 month weight-for-length chart, a 70 cm boy at the 50th percentile weighs approximately 8.42 kg (18.6 lb). A girl at the same length at the 50th percentile weighs approximately 7.97 kg (17.6 lb). The 50th percentile is the WHO median — half of same-sex children at that length weigh more, half weigh less — it is not a goal weight every child is expected to hit.

How is weight-for-length different from weight-for-age?

Weight-for-age compares the child's weight to peers of the same age; weight-for-length compares weight to peers of the same body length. A tall 12-month-old may be at the 90th on weight-for-age but only the 55th on weight-for-length — perfectly proportioned, just larger. A short 12-month-old may be at the 40th on weight-for-age but the 90th on weight-for-length — heavy for her body size even though her raw weight looks average. Pediatricians read both together, not in isolation.

Why does this calculator ignore age?

The WHO weight-for-length table is indexed by length only — the LMS parameters are looked up using the measured recumbent length in centimeters, not the child's age in months. This is deliberate: weight-for-length is designed to assess body proportionality independently of age, which is exactly what's useful when you want to know whether a child's weight is in balance with their body size. If you need an age-based read, use the WHO weight-for-age or length-for-age calculators.

What counts as wasting on the WHO weight-for-length chart?

WHO defines moderate wasting as a weight-for-length Z-score between −3 and −2 (roughly the 0.1st to 3rd percentile) and severe wasting as Z below −3. Overweight is defined as Z above +2 (approximately the 97th percentile). These cutoffs drive the WHO IMCI treatment guidelines and case-finding rules in both clinical and humanitarian settings, and are the reason weight-for-length below the 3rd percentile is the primary screen for acute malnutrition in children under 2.

When does a child transition from weight-for-length to weight-for-height?

Around age 2 (or once the child reliably stands still enough to be measured standing), pediatricians switch from the WHO 0-24 month weight-for-length chart (recumbent length) to the WHO 2-5 year weight-for-height chart (standing height). The two measurements differ by about 0.7 cm — standing height reads shorter than recumbent length in the same child — and WHO publishes separate reference data for each. Stay on one chart until the transition visit so percentiles don't jump artificially.

Should I measure recumbent length or standing height?

For children 0-24 months, this chart uses recumbent length — measured with the child lying flat on a length board, legs extended. Standing height is typically about 0.7 cm shorter than recumbent length in the same child, so using a standing measurement here will shift the percentile slightly downward. If your child is already being measured standing (common after about 24 months), use the WHO 2-5 weight-for-height chart instead for a clean match between the measurement and the reference.

What length range does this calculator cover?

The WHO 0-24 month weight-for-length table covers recumbent lengths from 45 cm to 110 cm (about 17.7 to 43.3 in). Lengths outside this range are not part of the WHO weight-for-length reference for 0-24 months. For taller children, switch to the WHO 2-5 year weight-for-height chart (standing height, 65-120 cm).

Are WHO and CDC weight-for-length charts the same?

No. The WHO chart is built from a breastfed international reference sample (the WHO Multicentre Growth Reference Study, 2006) and describes how children should grow under optimal feeding and care conditions — it is the AAP-recommended chart for children under 24 months. The CDC 2000 weight-for-length chart is built from US national survey data (1963-1994) and describes how US children historically grew; it is commonly used in the US for the full 0-36 month window. Pick one and stay consistent across visits to avoid artificial percentile jumps.

Reference: WHO Child Growth Standards: Weight-for-Length/Height. World Health Organization, 2006. https://www.who.int/tools/child-growth-standards

Worked Examples

Healthy proportion check

A boy 70 cm long weighing 8.5 kg — where does he fall?

A pediatrician is reviewing a healthy-term boy whose recumbent length is 70 cm and weight is 8.5 kg. The WHO weight-for-length chart ignores age entirely — the LMS lookup is purely by length.

  • Knowns: sex boy, length 70.0 cm, weight 8.5 kg
  • WHO LMS lookup at 70.0 cm (boys): L ≈ -0.3521, M ≈ 8.4227 kg, S ≈ 0.08171
  • Z = ((8.5 / 8.4227)^-0.3521 − 1) / (-0.3521 × 0.08171) ≈ 0.11
  • Φ(0.11) ≈ 0.54
  • Result: ~50th percentile — essentially at the WHO median weight for his length.

A single reading near the median is reassuring; pediatricians track whether the child continues along the same channel at subsequent visits.

US-units well-child visit

A girl 25 in long weighing 15 lb — what percentile?

A parent reports their daughter's recumbent length as 25 in and weight as 15 lb. The calculator converts both to the canonical units (25 in × 2.54 = 63.5 cm; 15 lb × 0.4536 = 6.80 kg) before the WHO LMS lookup.

  • Knowns: sex girl, length 25 in → 63.5 cm, weight 15 lb → 6.80 kg
  • WHO LMS lookup at 63.5 cm (girls) from the 0.1-cm WHO Anthro table
  • Z ≈ ((6.80 / M)^L − 1) / (L × S) ≈ 0.33
  • Φ(0.33) ≈ 0.63
  • Result: ~63rd percentile — modestly above median but well inside the healthy range.

Chart values are for recumbent length — a standing measurement would read about 0.7 cm shorter and shift the percentile slightly.

Wasting screen

A boy 80 cm long weighing 8.8 kg — is there a wasting concern?

A toddler presents at a follow-up visit measuring 80 cm long and 8.8 kg. Weight-for-length is the WHO IMCI primary screen for wasting (acute undernutrition) in children under 2.

  • Knowns: sex boy, length 80.0 cm, weight 8.8 kg
  • WHO LMS lookup at 80.0 cm (boys): L ≈ -0.3521, M ≈ 10.92 kg, S ≈ 0.08013
  • Z ≈ ((8.8 / 10.92)^-0.3521 − 1) / (-0.3521 × 0.08013) ≈ -2.47
  • Φ(-2.47) ≈ 0.007
  • Result: below the 1st percentile — past the −2 Z-score threshold WHO flags as wasting.

A single low reading warrants clinical assessment — nutrition history, illness, and growth trajectory together determine whether intervention is needed.

How the percentile is calculated

The calculator turns one pair of measurements — recumbent length and weight — into a percentile in three stages. First, it looks up three WHO parameters — L, M, and S — from the WHO Child Growth Standards weight-for-length (0-24 months) table at the child's exact recumbent length in centimeters. Age is not used — the independent variable on this chart is length, not time. L is the Box-Cox power transform that accounts for skew in the weight distribution at that length, M is the median weight of same-sex children at that length, and S is the coefficient of variation. Second, it plugs those parameters into the Z-score formula:

Z score equals the quantity X divided by M, raised to the power L, minus 1, divided by L times S.

Where:

  • X — the child's measured weight in kilograms.
  • M — the WHO median weight at that length and sex.
  • L — the Box-Cox skewness parameter at that length.
  • S — the coefficient of variation at that length.

Third, the Z-score is mapped to a percentile through the standard normal cumulative distribution function, Φ(Z). A Z of 0 maps to the 50th percentile, −1.88 to the 3rd, and +1.88 to the 97th. The WHO 0-24 month weight-for-length table spans lengths from 45 cm to 110 cm in one-millimeter (0.1 cm) steps, so fractional lengths resolve to the nearest row without interpolation. A child whose age falls outside the 0-24 month window but whose recumbent length still sits in this range can still be looked up — the chart is length-indexed, not age-indexed — though WHO recommends transitioning to the 2-5 year weight-for-height chart (standing height) around age 2.

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